Sen. Bob Corker (R-Tenn.), the ranking member on the committee, said that the U.S. should lead an international effort to halt Russia's military intervention in Ukraine, including sanctions on the Russian government of President Vladimir Putin.

“Vladimir Putin is seizing a neighboring territory — again — so President Obama must lead a meaningful, unified response with our European allies to bring an immediate halt to these provocative Russian actions, which threaten international peace and security. The Russian government has felt free to intervene militarily in Ukraine because the United States, along with Europe, has failed to make clear there would be serious, potentially irreparable consequences to such action,” Corker said in a statement.

“The United States and our European allies should immediately bring to bear all elements of our collective economic strength to stop Russian advances in Ukraine. Congress will consider targeted sanctions against Russian persons and entities that undermine the sovereignty and territorial integrity of Ukraine.”

Sen. Marco Rubio (R-Fla.), a member of the Foreign Relations Committee, said the developments were "deeply concerning," calling Putin a "tyrant" in a terse statement.

"The U.S. cannot accept Russian aggression against a neighbor and United Nations member in blatant violation of international law. Now is the time for U.S. leadership," Rubio said.

"The U.S. and the European Union should take meaningful measures to demonstrate to the Russian government that military action against Ukraine is intolerable and will carry significant consequences for Moscow."

On Friday, Obama said that any Russian military intervention would have "costs." Sen. John McCain (R-Ariz.) said Obama needs to outline those costs, now that Russia's parliament has approved the use of the country's military in Ukraine.

"Every moment that the United States and our allies fail to respond sends the signal to President Putin that he can be even more ambitious and aggressive in his military intervention in Ukraine," McCain said in a statement.

"There is a range of serious options at our disposal at this time without the use of military force. I call on President Obama to rally our European and NATO allies to make clear what costs Russia will face for its aggression and to impose those consequences without further delay."